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We propose a novel Bayesian optimization framework for situations where the user controls the computational effort and therefore the precision of the function evaluations. This is a common situation in econometrics where the marginal likelihood is often computed by Markov chain Monte Carlo or importance sampling methods. The new acquisition strategy gives the optimizer the option to explore the function with cheap noisy evaluations and therefore find the optimum faster. The method is applied to estimating the prior hyperparameters in two popular models on US macroeconomic time series data: the steady\u2010state Bayesian vector autoregressive (BVAR) and the time\u2010varying parameter BVAR with stochastic volatility.<\/jats:p>","DOI":"10.1002\/jae.2961","type":"journal-article","created":{"date-parts":[[2023,1,28]],"date-time":"2023-01-28T07:34:46Z","timestamp":1674891286000},"page":"577-595","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Bayesian optimization of hyperparameters from noisy marginal likelihood estimates"],"prefix":"10.1002","volume":"38","author":[{"given":"Oskar","family":"Gustafsson","sequence":"first","affiliation":[{"name":"Department of Statistics Stockholm University  Stockholm Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mattias","family":"Villani","sequence":"additional","affiliation":[{"name":"Department of Statistics Stockholm University  Stockholm Sweden"},{"name":"Department of Computer and Information Science Link\u00f6ping University  Link\u00f6ping Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P\u00e4r","family":"Stockhammar","sequence":"additional","affiliation":[{"name":"Department of Statistics Stockholm University  Stockholm Sweden"},{"name":"Sveriges Riksbank  Stockholm Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2023,2,27]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/07474930701220121"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/07474930701220071"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/jae.1137"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/141000671"},{"key":"e_1_2_9_6_1","unstructured":"Brochu E. 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